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A NOTE ON THE MULTILINEAR SINGULAR INTEGRAL OPERATORS
作者单位:University of Information Engineering,China
摘    要:Lp(Rn) boundedness is considered for the multilinear singular integral operator defined by TAf(x) = ∫Rn Ω(x - y)/|x - y|n 1 (A(x) - A(y) - (△)A(y)(x - y))f(y)dy,where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(Rn). We give a smoothness condition which is fairly weaker than that Ω∈ Lipα(Sn-1) (0 <α≤ 1) and implies the Lp(Rn) (1 < p < oo) boundedness for the operator TA. Some endpoint estimates are also established.

关 键 词:多线性奇异积分算子  零度均匀  端点估计  光滑条件  BMO

A note on the multilinear singular integral operators
Authors:Jiao Yulan
Institution:(1) College of Science, University of Information Engineering, P. O. Box 2201-160, 450001 Zhengzhou, P. R. China
Abstract:L p (R n ) boundedness is considered for the multilinear singular integral operator defined by

$$T_A f(x) = \smallint _{\mathbb{R}^n } \frac{{\Omega (x - y)}}{{|x - y|^{n + 1} }}(A(x) - A(y) - \nabla A(y)(x - y))f(y)dy$$
where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one. A has derivatives of order one in BMO(R n ). We give a smoothness condition which is fairly weaker than that Ω∈Lip α(Sn−1) (0<α⪯1) and implies theL p (R n ) (1<p<∞) boundedness for the operator TA. Some endpoint estimates are also established.
Keywords:multilinear singular integral operator  homogeneous of degree zero  smoothness condition  SINGULAR INTEGRAL OPERATORS  estimates  established  singular integral operator  smoothness condition  derivatives  integrable  the unit sphere  moment  order  homogeneous of degree zero  boundedness  defined
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